Randomize wave texture rotation
You can use the Object Info Random Output as an angle for rotation of the texture in one or more axis. I understand your problem is that the mapping nodes doesn't have input, you can however use rotation transformation matrices to compute the vector manually, in one axis (z), it looks like this:



In three dimensions you can use the 3D Rotation Transformation Matrices to get:



The node tree is big, so here is the file to study it: